The dielectric constant, also called relative permittivity (εr), is the factor by which the electric field between the charges is decreased relative to vacuum. The relative permittivity of vacuum is equal to 1. The relative permittivity is a complex quantity. The imaginary part corresponds to a phase shift of the polarization density (P) relative to the electric field (E) and leads to the attenuation of electromagnetic waves passing through the medium.
The precise measurement of dielectric constant of the material is needed to design all the engineering products which utilized the dielectric materials. Dielectrics are introduced in capacitors to increase the capacitance. Dielectrics are also used in transmission lines like in coaxial cables. Polyethylene is a popular material that is used in between the center conductor and outside shield in coaxial cables. Dielectric materials are also placed inside waveguides to form filters and enhance the cut-off frequencies of different propagation modes. Optical fibers are prime examples of dielectric waveguides. The relative permittivity of dielectric materials changes with temperature, humidity, and pressure. Different types of sensors can be constructed to detect changes in capacitance caused by changes in the relative permittivity.
The complex dielectric constant (or the relative permittivity) of a dielectric material has an imaginary part and a real part and can be expressed as εr(1+j tan δ) where the loss tangent is the ratio of the imaginary part to the real part. There are multitude of the methods and procedure available to measure the static dielectric constant (at Zero frequency) and at different frequencies as well. There are wideband and narrowband methods. The traditional wideband methods scan a large frequency band and hence require extensive measurement setups which are expensive, hard to calibrate and maintain. The traditional resonator based (narrowband) methods require the determination of the complex dielectric constant by measuring the resonance frequency and the resonance bandwidth from the magnitude (amplitude) spectrum of the microwave device that contains the dielectric sample. The traditional wideband methods require the measurement of both the magnitude and the phase for determining the dielectric constant. Hence they are more complex and expensive. Furthermore, accurate calibration of the measurement equipment is needed both for the measurement of magnitude and phase to measure the true value of the absolute magnitude and absolute phase.